# gsw_t_freezing

`in-situ temperature freezing point`

## USAGE:

`t_freezing = gsw_t_freezing(SA,p,saturation_fraction)`

## DESCRIPTION:

```Calculates the in-situ temperature at which seawater freezes. The
in-situ temperature freezing point is calculated from the exact
in-situ freezing temperature which is found by a modified Newton-Raphson
iteration (McDougall and Wotherspoon, 2013) of the equality of the
chemical potentials of water in seawater and in ice.```
```An alternative GSW function, gsw_t_freezing_poly, it is based on a
computationally-efficient polynomial, and is accurate to within -5e-4 K
and 6e-4 K, when compared with this function.```

## INPUT:

```SA  =  Absolute Salinity                                        [ g/kg ]
p   =  sea pressure                                             [ dbar ]
( i.e. absolute pressure - 10.1325 dbar )

OPTIONAL:

saturation_fraction  =  the saturation fraction of dissolved air
in seawater
(i.e., saturation_fraction must be between 0 and 1, and the
default is 0, air free)

p & saturation_fraction (if provided) may have dimensions 1x1 or Mx1
or 1xN or MxN, where SA is MxN.```

## OUTPUT:

```t_freezing = in-situ temperature at which seawater freezes.    [ deg C ]
(ITS-90)           ```

## EXAMPLE:

```SA = [34.7118; 34.8915; 35.0256; 34.8472; 34.7366; 34.7324;]
p =  [     10;      50;     125;     250;     600;    1000;]
saturation_fraction = 1;```
`t_freezing = gsw_t_freezing(SA,p,saturation_fraction)`
`t_freezing =`
```  -1.902730710149803
-1.942908619287183
-2.006861069199743
-2.090985086875259
-2.351293130342102
-2.660498762776720```

## AUTHOR:

`Paul Barker, Trevor McDougall and Rainer Feistal    [ help@teos-10.org ]`

## VERSION NUMBER:

`3.05 (16th February, 2015)`

## REFERENCES:

```IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of
seawater - 2010: Calculation and use of thermodynamic properties.
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
UNESCO (English), 196 pp.  Available from the TEOS-10 web site.
See section 3.3 of this TEOS-10 Manual.```
```McDougall, T.J., P.M. Barker, R. Feistel and B.K. Galton-Fenzi, 2014:
Melting of Ice and Sea Ice into Seawater and Frazil Ice Formation.
Journal of Physical Oceanography, 44, 1751-1775.```
```McDougall, T.J. and S.J. Wotherspoon, 2013: A simple modification of
Newtonâ€™s method to achieve convergence of order "1 + sqrt(2)". Applied
Mathematics Letters, 29, 20-25.
http://dx.doi.org/10.1016/j.aml.2013.10.008 ```
`The software is available from http://www.TEOS-10.org`